1x^6-10x^4+32x^2+000=0

Solution for 1x^6-10x^4+32x^2+000=0 equation:

Simplifying
1x6 + -10x4 + 32x2 + 0 = 0

Reorder the terms:
0 + 32x2 + -10x4 + 1x6 = 0
Remove the zero:
32x2 + -10x4 + 1x6 = 0

Solving
32x2 + -10x4 + 1x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(32 + -10x2 + x4) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(32 + -10x2 + x4)' equal to zero and attempt to solve:

Simplifying
32 + -10x2 + x4 = 0

Solving
32 + -10x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -10x2 + -32 + x4 = 0 + -32

Reorder the terms:
32 + -32 + -10x2 + x4 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -10x2 + x4 = 0 + -32
-10x2 + x4 = 0 + -32

Combine like terms: 0 + -32 = -32
-10x2 + x4 = -32

The x term is -10x2.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x2 + 25 + x4 = -32 + 25

Reorder the terms:
25 + -10x2 + x4 = -32 + 25

Combine like terms: -32 + 25 = -7
25 + -10x2 + x4 = -7

Factor a perfect square on the left side:
(x2 + -5)(x2 + -5) = -7

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}